Question

16,820 rupees is divided between Govind and Geeta, both aged 27 and 25 years respectively. Their money is invested at 5% per annum compound interest in such a way that both receive equal money at the age of 40 years. Find the share of each out of 16,820 rupees.

Answer 1

Hint: In the above question, is based on the concept of compound interest. The main approach towards solving the question is to find out the individual share of Govind and Geeta from the amount 16820 by calculating the individual time period by applying 5% compounding interest.

Complete step-by-step answer:
The amount 16,820 is distributed among Govind and Geeta. So, let Govind share of money be x and then share of Geeta is 16,820-x. The interest rate per annum is 5%.
The age of Govind and the age of Geeta is 27 and 25 years respectively.
Therefore, time period for Govind=40-27=13 years
Therefore, time period for Geeta =40-25=15 years
At the age of 40 years both receive the same or equal amount.
Since we know the formula
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\]
Since the amount is equal at age 40 we can write as follows,
Share of Govind =Share of Geeta
\[x{\left( {1 + \dfrac{5}{{100}}} \right)^{13}} = \left( {16820 - x} \right) \times {\left( {1 + \dfrac{5}{{100}}} \right)^{15}}\]
Dividing by \[{\left( {1 + \dfrac{{15}}{{100}}} \right)^{13}}\]we get,
  $ \Rightarrow x = \left( {16820 - x} \right) \times {\left( {1 + \dfrac{5}{{100}}} \right)^2} $
  $ \Rightarrow x = \left( {16820 - x} \right) \times 1.1025 $
  $ \Rightarrow 2.1025x = 18544.05 $
  $\Rightarrow x = 8820 $

Therefore, Govind’s share=8820rupees
Geeta’s share=16820-8820=8000 rupees.

Note: An important thing to note is that interest is applied from both Govind and Geeta’s age 27 and 25 till the age of 40.Once both reach at the age of 40 after 5 % of compounding interest every year they receive equal money.